What does this mean: "Tis but thy name that is my enemy Thou art thy self, though not a Montague. O be some other name"? act 2 scene 2

I totally agree but to fully understand these words, it is
necessary to look at the whole speech and the context of that
speech.

When she says this, she does not know that Romeo is
eavesdropping on her spoken thoughts.

When she woke up that
morning, she was a normal nearly fourteen year old girl.  In the afternoon, she is told
by her mother that her father has talk to young Paris who wishes to marry her.  She
urges Juliet look upon him with favor that night at the mask ball.  She then meets a
young man that for some reason she is attracted to only to find out that the young man
she is interested in is a Montague, the family's arch
enemy.

It is in this speech that she says, "...That which
we call a rose/By any other name would smell as
sweet:..."

For the first time in her young life, Juliet
questions what she has been told her entire life.  She realizes that judging somebody
because of their name or by extension religion, color, culture, tribe, etc. is stupid. 
When analysed, it doesn't make any sense.